Extra Problems Chapter 10 - AEB 3510 Extra Problems Chapter...

AEB 3510, Extra Problems Chapter 9
1. The Total Revenue function for a milk producer is given by
TR(Q) = -0.1Q 2 +4.5Q +35,
Where Q is the quantity of milk demanded (in pounds) and P is the unit price of milk.
a) Find the derivative of the Total Revenue function. What economic concept does this
derivative represent?
b) What is the rate of change in total revenue when the quantity demanded is 15 units?
2. Suppose that a (non-linear) supply function for a certain good is given by
p(Q) = 0.0001Q 3 +10,
Where Q is the quantity supplied and p is the unit price in dollars.
a) Is this an economically relevant supply relation (i.e., does the supply function make
economic sense?)?
b) Find the derivative of the supply function.
c) Find the slope of the supply function if the quantity supplied is 12000.
3. Retail revenue each year from internet shopping is approximated by the function
TR(t) = 0.075t 3 + 0.025t 2 +2.4
Where TR(t) is measured in billions of dollars and t is measured in years, with t = 0 corresponding to the
beginning of the year 2000.
a) Find an expression giving the rate of change of the retail revenue /year from internet
shopping at any time t.